Falconi will take on fifth-seeded Ana Ivanovic and Radwanska will face Venus Williams, the 16th seed.

Nicole Vaidisova moved on by handling Timea Babos 6-1, 7-6 (7-4). Vaidisova, 25, retired from the WTA in 2010, but decided to return to the courts last year and has now played in two WTA-level events so far in 2015, going 1-1. She will play the No. 3 seed, Simona Halep, in the second round, following Halep's win at Indian Wells over the weekend.